Roughness Model of Radar Backscattering From Bare Soil Surfaces

Amimul Ehsan

Electrical Engineering and Computer Science Department,

University of Kansas

April 29, 2015

2

Outlines

Motivation and Objective

Introduction

Surface Roughness

Backscattering Roughness Model

Results and Discussions

Reference

3

Motivation and Objective

Radar Backscattering is affected by three target features namely

surface roughness, vegetation and soil moisture. To get the effect of

any particular feature, other two need to be subtracted from the

measured backscattering.

The main goal of this study is to determine the dependence of radar

backscatter on roughness parameter.

Three models namely Physical Optics Model, Geometric Optics

Model and Small perturbation Model are studied for backscattering.

4

Introduction

When microwave EM energy

transmitted by a RADAR

system reaches the earth

surface, some is absorbed by

the surface and the remainder

is reflected in multiple

directions.

These surface reflections are

referred to as scattering of

microwave EM energy.

The microwave EM energy that is scattered in the Radar’s direction of

transmission is the only EM energy that is detected by the radar – this EM energy

is referred to as microwave or radar backscatter

Fig. Schematic view of scattering geometry [3]

5

Surface Roughness

Rough surface corresponds to Gaussian distribution.

𝐼 𝑠 (𝜃 )=𝐼 𝑠0|𝑅0 (𝜃 )|2𝑒𝑥𝑝 (−h𝑐𝑜𝑠2𝜃 )

𝑊 (𝑧 )= 1

𝜎 (2𝜋 )1 /2 𝑒𝑥𝑝 (−𝑧 2/2𝜎2 )

where, the scattered intensity with roughness parameter,

Surface roughness depends on standard deviation of height, and correlation length, . Here, corresponds to the vertical scale roughness and corresponds to the horizontal scale roughness.

Surface roughness types

Fig. Schematic of types of surface roughness [3]

6

Physical Optics Model

This model predicts the incoherent backscattering coefficient for a given surface.

where, is the incident angle 𝑘𝜎<0.3𝑜𝑟 𝜎<0.048 λ

𝑟𝑚𝑠 𝑠𝑙𝑜𝑝𝑒<0.25

𝜎 𝑖𝑛𝑐0 (𝜃 )=(𝑘𝑙 )2 [|𝑅𝑝𝑝|

2 (1+𝑠𝑖𝑛2𝜃 )+𝑅𝑒 (𝑅𝑝𝑝 𝑅𝑝𝑝 1∗ ) 𝑠𝑖𝑛2 𝜃 ]×𝑒−h𝑐𝑜𝑠2 𝜃∑

𝑛=1

∞ (h𝑐𝑜𝑠2𝜃 )𝑛

𝑛 !𝑛×𝑒

−(𝐾𝑙𝑠𝑖𝑛 𝜃 )2

𝑛

is the wave number in air

is the reflectivity of smooth surface

Conditions under this model applicable,

𝐾𝑙>6

7

Geometric Optics Model

This model has the form,

(2𝐾 𝜎 𝑐𝑜𝑠𝜃 )2>10

𝜎𝐻𝐻0 (𝜃 )=[|𝑅𝐻𝐻 (𝜃 )|2/ ( 2𝑚2𝑐𝑜𝑠2𝜃 )]×𝑒(− 𝑡𝑎𝑛

2 𝜃2𝑚2 )

where, is the reflectivity is the RMS surface slope and

Conditions of this model,

𝐾𝑙>6

8

Small Perturbation Model

This model has the form,

𝑘𝜎<0.3𝑜𝑟 𝜎<0.048 λ

𝑟𝑚𝑠 𝑠𝑙𝑜𝑝𝑒<0.3𝑜𝑟 𝜎<0.21 𝑙

𝜎𝐻𝐻=8𝐾 4𝜎2𝑐𝑜𝑠4 𝜃|𝑅𝐻|2[ 1

2 𝑙2 𝑒− (𝑘𝑙𝑠𝑖𝑛 𝜃 )2]

Surface roughness that has a Gaussian correlation function,

ρ (ζ )=exp−( ζ2

𝑙2 )This model can be used for,

𝐾𝑙<6

9

Roughness Effect on Backscattering

Physical Optics and Geometric Optics Model

Fig. Backscattering of Physical Optics Model by varying the roughness parameter

Fig. Backscattering of Geometric Optics Model by varying the roughness parameter

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Roughness Effect on Backscattering

Small Perturbation Model

Fig. Backscattering of Small Perturbation Model by varying the roughness parameter

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References

[1] Engman, Edwin T.; Wang, J.R., "Evaluating Roughness Models of Radar Backscatter," IEEE Transactions on Geoscience and Remote Sensing, vol.GE-25, no.6, pp.709,713, Nov. 1987

[2] Yisok Oh; Sarabandi, K.; Ulaby, F.T., "An empirical model and an inversion technique for radar scattering from bare soil surfaces," IEEE Transactions on Geoscience and Remote Sensing, vol.30, no.2, pp.370,381, Mar 1992

[3] Tsan Mo, Thomas J. Schmugge, Thomas J. Jackson, “Calculations of radar backscattering coefficient of vegetation-covered soils,” Remote Sensing of Environment, Volume 15, Issue 2, March 1984, Pages 119-133

[4] F. T. Ulaby, R. K. Moore, and A. K. Fung, 1986, Microwave Remote Sensing Active and Passive. Dedham, MA: Artech House, 1986, vol. 3.

[5] Zribi, M.; Gorrab, A.; Baghdadi, N., "A new soil roughness parameter for the modelling of radar backscattering over bare soil," Geoscience and Remote Sensing Symposium (IGARSS), 2014 IEEE International , vol., no., pp.3378,3381, 13-18 July 2014.

[6] Choudhury, B. J., T. J. Schmugge, A. Chang, and R. W. Newton (1979), Effect of surface roughness on the microwave emission from soils, J. Geophys. Res., 84(C9), 5699–5706, 

[7] D.L. Evans, T.G. Farr and J. J. van Zyl, "Estimates of surface roughness derived from synthetic aperture radar (SAR) data, " IEEE Transactions on Geoscience and Remote Sensing, vol. 30, pp. 382-389, 1992.